|
%I #22 Jun 19 2019 17:56:39
%S 1,3,1,3,3,4,1,5,6,6,1,7,3,4,8,1,3,9,3,5,10,1,11,10,6,12,1,13,3,7,14,
%T 1,3,5,15,3,4,8,16,1,17,6,6,9,18,1,19,3,9,10,20,1,3,7,21,3,11,22,1,23,
%U 10,6,8,12,24,1,5,25,3,13,26,1,3,9,27,3,4,7,14,28
%N Triangle read by rows: T(n,k) = sum of the k-th divisor island of n.
%C A divisor island is any set of consecutive divisors of a number where no pairs of consecutive divisors in the set are separated by 2 or more.
%C For the number of divisor islands of n see A137921.
%C Row n has length A137921(n).
%C Row sums give A000203.
%C T(n,1) is a positive triangular number.
%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F T(n,k) = A027750(n,k), if A137921(n) = A000005(n).
%e Written as an irregular triangle the sequence begins:
%e 1;
%e 3;
%e 1, 3;
%e 3, 4;
%e 1, 5;
%e 6, 6;
%e 1, 7;
%e 3, 4, 8;
%e 1, 3, 9;
%e 3, 5, 10;
%e 1, 11;
%e 10, 6, 12;
%e 1, 13;
%e 3, 7, 14;
%e 1, 3, 5, 15;
%e 3, 4, 8, 16;
%e 1, 17;
%e 6, 6, 9, 18;
%e 1, 19;
%e 3, 9, 10, 20;
%e ...
%e For n = 20 and k = 2 the divisors of 20 are [1, 2, 4, 5, 10, 20], there are four divisor islands: [1, 2], [4, 5], [10], [20] and the sum of the second divisor island is 4 + 5 = 9, so T(20,2) = 9.
%Y Cf. A000203, A000217, A027750, A137921.
%K nonn,tabf
%O 1,2
%A _Omar E. Pol_, Jul 24 2014
|
